Though the juggernaut musical “Hamilton” is bursting with facts and figures from the American Revolution, there’s a whole other, less obvious history that underlies its every performance. No, I am not hinting at the existence of coded conspiracy messages involving the Illuminati. (But apparently, if you play the song “The Reynolds Pamphlet” backward. …)

What I’m talking about is a war that has been waged tirelessly for more than a century: the fight to be perceived as the sole musical left standing tall in the battlefield called Broadway. And if you hope to understand the role of “Hamilton” within this epic struggle, you are earnestly advised to attend the (highly) animated dissertation on the subject, titled “Spamilton,” which opened on Thursday night at the Triad.

This smart, silly and often convulsively funny thesis, performed by a motor-mouthed cast that is fluent in many tongues, is the work of that eminent specialist in Broadway anatomy, pathology and gossip, Gerard Alessandrini. As the creator of the “Forbidden Broadway” series of satirical revues, which began in 1982, Mr. Alessandrini has emerged as one of the mainstream musical’s most incisive and illuminating critics and historians.

If you weren’t aware of such academic acumen while you were watching his revues, it was because you were laughing too hard. But to this day, I find that when I think of certain shows — whether they’re hits like “Les Misérables” and “Spring Awakening,” or flops like “Aspects of Love” and “Big” — it’s the “Forbidden Broadway” spoof that first surfaces in my memory.

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Dan Rosales, left, and Chris Anthony Giles in “Spamilton.”CreditSara Krulwich/The New York Times

Now Mr. Alessandrini — as writer, director and song mangler — has trained his unsparing eye on Lin-Manuel Miranda’s “Hamilton,” the rap-driven, trophy-laden portrait of the American founding fathers that has so dominated commercial theater of late that you could be excused for believing it was the only show in town. “Spamilton” emphasizes this point by recreating the climactic moment at the last Tony Awards ceremonies, when Barbra Streisand presented the statue for best musical. In this version, Ms. Streisand (reincarnated with blissfully buttery smoothness by the recent University of Michigan graduate Nora Schell, a name to watch) reads the nominees: “‘Hamilton,’ ‘Hamilton,’ ‘Yentl’ — oh, sorry — I mean ‘Hamilton’ and ‘Hamilton.’”

But contrary to what its more rabid fans might believe, “Hamilton” is neither the only show in town nor the only musical that ever mattered. “Spamilton” is here to dispel those myths by placing Mr. Miranda’s masterwork in a context that might be described, on many levels, as broad.

In other words, Mr. Alessandrini’s latest effort isn’t just about “Hamilton,” but about where it fits on the continuum of show business as usual. This means that in addition to presenting Mr. Miranda (the original leading man, as well as the creator, of “Hamilton”) and his co-stars with quick, evocative strokes worthy of an Al Hirschfeld caricature, “Spamilton” makes room for a galaxy of other stars.

They include divas as different as Bernadette and Beyoncé, Liza and J Lo. (And if those names don’t ring a bell, “Spamilton” is not your show.) Such diversity testifies to the status of “Hamilton” as a colossal straddler of the worlds of classic musicals and contemporary pop. And its revered status is signaled by the presence of the husband and wife who begin “Spamilton” by putting on the “Hamilton” cast recording as they slip into bed: Barack and Michelle Obama.

Mr. Alessandrini explains in a program note that the first couple’s affection for the show brought to mind the relationship of another American president, John F. Kennedy, to another musical, “Camelot,” whose score (according to Jacqueline Kennedy) he liked to listen to before he went to sleep. Hence the Obamas in their pjs by way of an overture for “Spamilton.” What follows, Mr. Alessandrini writes, is a “mash-up of theater today and my wildest musical comedy dreams.”

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From left, Chris Anthony Giles, Nicholas Edwards, Juwan Crawley and Nora Schell in Gerard Alessandrini’s spoof of “Hamilton.”CreditSara Krulwich/The New York Times

Mr. Miranda presumably dreamed such dreams himself. Portrayed here as a relentlessly intense prodigy and a nerd to remember by Dan Rosales, he sings (or rather raps) about the musical comedy soundtrack of his childhood and his horror at what Broadway had become beneath the Technicolor shadow of Disney. For the repeated “Hamilton” lyrics “I am not throwing away my shot,” Mr. Alessandrini has substituted “I am not gonna let Broadway rot.”

And so we see Mr. Miranda creating “my own revolution, a hop hip solution.” Its versatile participants include Chris Anthony Giles (doing Leslie Odom Jr. doing Aaron Burr), Nicholas Edwards (doing Daveed Diggs doing Thomas Jefferson and Marquis de Lafayette) and Juwan Crawley (who, in an inspired interpolation, does a Yoda-like Stephen Sondheim doing Benjamin Franklin). The show also has two uncredited guest stars who appear vividly as ghosts of Broadway past, all accompanied with brio by the show’s pianist and musical director, Fred Barton.

Featuring witty shorthand choreography (“Thighs up!”) by Gerry McIntyre and costumes by Dustin Cross, “Spamilton” covers a lot of territory in its 70 minutes. It lays siege to “Hamilton”-related matters of commerce (those ticket prices!), sexuality (bye-bye to the gay White Way), the stoner sensibility and the incomprehensibility of its rapid-fire lyrics. (Thomas Jefferson’s number “What Did I Miss?” is reinvented as “What Did You Miss?”)

Those who know their “Hamilton” will especially savor the meticulously warped mirror images of specific numbers. (Eliza Hamilton’s soaring aria of heartbreak and dense synopsis at the show’s end is hilariously rendered here as “Who Lives, Who Dies, Who Cries.”) Other theatergoers may not get many of the jokes, particularly since “Spamilton” sometimes lacks the precision (and the diction) of its prototype.

But more than any of Mr. Alessandrini’s portmanteau spoofs, “Spamilton” has an energizing, free-associating euphoria that follows one theater obsessive’s prismatic “mind at work” (to borrow a “Hamilton” lyric). Given that “Hamilton” is itself a master at mixing anachronistic sensibilities, it feels appropriate that the fever dreams of “Spamilton” turn into surreal Broadway musical mash-ups. Among their titles: “An American Psycho in Paris” and “The Lion King and I.”

Such anarchic whimsy exists with cooler, savvy appraisals of how “Hamilton” is different from, and similar to, its predecessors and displaced rivals (sorry, “Book of Mormon”), as well as of what the future holds for this supernova show. The ersatz Ms. Streisand is only pondering the inevitable when she sings, in a nod to the best-known song from “Hamilton,” “I wanna be in the film when it happens.”